From the Wookieepedia page on the word "Darth":
From the "Canon" page:
Darth was a title given to the Dark Lords of the Sith Order, which preceded a moniker different from the birth name. The Sith names of Sheev Palpatine, Dooku and Anakin Skywalker were Darth Sidious, Darth Tyranus and Darth Vader. The title was already in use about one millennium before the Clone Wars, when Darth Bane created the Rule of Two. In at least one known case, that of Anakin Skywalker, the Darth title and the accompanying moniker were bestowed onto the Sith apprentice by the master. The Jedi Master Obi-Wan Kenobi once used "Darth" as a form of address when talking to Darth Vader. It was traditional that only the current Sith Master and his or her apprentice were allowed to use the Darth title.
From the "Legends" page:
Many Sith Lords chose to add "Darth" to their name, so much so that the word is considered synonymous with the dark side of the Force in some circles. It was also taken to signify giving up one's old life. Such examples are Anakin Skywalker becoming Darth Vader, or Jacen Solo becoming Darth Caedus. But the origins of the word are uncertain. It is often thought that "Darth" is merely a contraction of the title "Dark Lord of the Sith", but there are theories that suggest a deeper interpretation.
From the "Behind the Scenes" section:
Darth is often thought to be a combination of letters from the title Dark Lord of the Sith, a theory which is alluded to in Jedi vs. Sith: The Essential Guide to the Force. Darth may also be a portmanteau of dark and death.
Prior to the release of The Phantom Menace, the only known Sith Lord to bear the title Darth was Darth Vader. When Darth Sidious and Darth Maul were revealed in The Phantom Menace, the title took on its distinct association with the Sith, and it has appeared throughout of all eras of the Star Wars saga. As a result of the popularity of Star Wars, the term "Darth" has entered the popular lexicon as a term for evil. Most references are still associated with the Star Wars universe.
In A New Hope, Obi-Wan Kenobi addresses Darth Vader simply as Darth, which is the only instance in the films where the word is used isolated. It is possible that at this point in the development of the saga "Darth" was intended to be the character's name, not a title; in-universe, possibly Obi-Wan was deliberately emphasizing the title as a way of taunting Vader and driving home what he had become.